The ranchu originates from Japan while the lionhead originates from China. I think lionheads are the older breed.
Lionheads have shorter bodies, thinner heads but bigger wens, and grow smaller. Their tails are also not tucked under their bodies as much..
(ex from Fish Sempai, Canadian breeders)

There are two types of ranchu, top view and side view. Ranchu in general grow larger, have a more rectangular head (most important in top views) and the tail is tucked under the body more.
(top view ranchus from Fish Sempai also)

(a side view, showing the tail tuck, again from Fish Sempai).

Generally, the ones sold in pet stores can be either way.. they are not show quality so don't display the traits of show quality fish, it's hard to say what the fish you get in the pet store is, where they use the two names interchangeably.